Which way does the box exit the portal?

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Wouldn't it be A because the cube dosent have any momentum and that's what transfers between the portals?
Momentum is a relative quantity, so from the plate's frame of reference the cube does have momentum.

I would presume that B is the answer, at least within the rules of portal.
 
I think it's probably something in between. There would be some momentum, at least enough to get the box off the ramp, but it's not going to be a whole lot.

There are a ton of other factors at play, like what kind of press is that, how fast is it moving, how is the box hovering over the portal and not just falling into it, and if it's rotated just enough to balance two corners on the rim of the orange portal, and the press is pushing it through by damaging the cube itself, that could definitely impart an amount of momentum through the blue portal.
 
Momentum is a relative quantity, so from the plate's frame of reference the cube does have momentum.

I would presume that B is the answer, at least within the rules of portal.
Relative to the portal, you can think of the first image as the bottom platform moving towards the portal. In that context it makes sense for there to be momentum coming out. Regardless if it was the box or portal moving originally, the box entered the portal at a fast speed, meaning that when it comes out that speed will be maintained
 
It's A.
A portal is essentially just a hole that leads from one place to a disconnected one. Imagine if you just drilled a hole in the middle of the press and looked through it as it fell on the box's holding plate, the box doesn't move. That's what you would see if you looked through the exit portal in this scenario.
 
A. "Momentum, a function of mass and velocity, is conserved between portals. In layman's terms: speedy thing goes in, speedy thing comes out." (via GLaDOS)

We can assume then that if a slow thing goes in, a slow thing comes out, as happens in Portal with the player.
 
The force from the plate with the in-portal should effect the rate the box enters the portal, so that force should effect how box exits. I'm assuming that portals take in conservation of momentum to be the rate matter enters the ports, so it shouldn't really matter if the force is applied the port or the box going though it.
A. Otherwise the earth's own speed of rotation would be taken into account.
The box, both ends of the port, and the world are all traveling at the same speed on the planet when the box enters the portal. Portals transport matter instantaneously, so there is no time for the box to be dis-affected by the lack of Earth's gravity while inside the portal. An object exiting a portal would tend to fall back into the portal, if the two portals were not going at the same speed. The object entering would have to catch back up to Earth's speed on exiting the portal, so it would need to be taken into account.
Wouldn't it be A because the cube dosent have any momentum and that's what transfers between the portals?
The platform has acceleration, so the relative momentum of the cube to the platform is negative (deceleration), so there still is momentum in the cube too. The cube's momentum is stationary relative to an observer also on the planet. But the the platform, the cube is moving towards the platform, if we pretend that all we can observer is from the platforms point of view. Then the platform should appear stationary and the cube is moving towards the platform.

This is actually really interesting, to summarize:
  • Do portals work off the rate that matter enters them?
  • Do portals transport only the force stored inside matter that enters them?
I really think option B has to be correct. When you are in a room on Earth with a in-portal you, the portal the room are all moving at the speed of Earth's rotation and when you walk through a portal there is no difference is Earth's effects on you or the portal. You are both moving at he same rate relative to Earth so it seems like the portal is stationary. Now imagine you were in a large room in a helicopter and you are trying to throw a box though a portal. You in the helicopter are not moving a the same rate as the in-portal and the out-portal and the Earth. You in the helicopter holing a constant position are now moving at a different relative rate compared to the earth, so the earth and portals will move around you. Now you are on the ground ready to walk though the a portal like usual. If the portal only cared about the speed at which objects entered, then the speed of the wall the portal is on would work against you. You would enter the portal at one speed, become move into a space not sharing the acceleration of the Earth while stepping though, and then have a new rate of relative momentum to the Earth when you entered the other side. It's just like the helicopter, you wouldn't be at the same relative speed of the Earth so the Earth would be moving around you. There would be more problems if A were true. You whole body wouldn't be at a constant speed when you are walking though a portal because the portal would only be moving your speed and not the relative speed. You relative speed is the Earth's speed and your speed. Earth's speed would cease to effect you once you stepped though and half way though would would be fighting to match the speed of the Earth exiting the out-portal. What would likely happen is you would fall back into the in-portal you entered. This would be caused by the different speeds. Since the out-portal doesn't care what speed it's moving at you relative speed wouldn't be matched with the Earth's and your situation would be like in the helicopter example where the Earth is moving independently form you or the helicopter.
 
It should be impossible to have a portal on a moving surface anyway.
I'm going to ignore the part of the game where you do place portals on moving platforms in the neurotoxin chambers, it goes against everything learned before that and it's the only moment where it's possible.
 
A. It's got to be A. It would work the same as this old gag:
I think you've hit the nail on the head. A portal is ultimately just a hole, so if something with a portal on it were to fall on you and you were hit only by the portal, you'd just be being hit by the hole in the object. That is to say, the object misses you entirely, and doesn't influence your speed or direction.
 
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